Abstract

1. Introduction

2. Theory

Spectropolarimetry is two observational techniques in one: spectroscopy and polarimetry. Spectroscopy is the study of an object's spectrum, through which it is possible to determine the composition of the object by identifying emission and absorption features caused by various elements and molecules. Polarimetry is the study of how the light emitted by or passing through an object is polarized, or more simply, the orientation and amplitude of vibration of the light as it travels through space.

2.1 Polarization In YSOs

Many young stellar objects (YSOs) are embedded in a dense molecular cloud consisting of dust grains, which are composed of silicates and carbonaceous material. On these grains water ice, either pure or contaminated with other molecules (in a mixture referred to as ``astronomical ice'') can form a mantle, coating the grains. These grains then become spun up with the spin axis perpendicular to the long axis¹. A magnetic moment is subsequently induced in the spinning grain along the long axis in a process known as the Barnett effect. If the magnetic moment (and thus the long axis of the grain) is not oriented perpendicularly to the external magnetic field, the magnetic moment does work against this external magnetic field as the grain spins. However, if the magnetic moment is perpendicular to this magnetic field, no work is done as the grain spins. As a system in which no work is done is preferable to one in which work is done, the long axis of the grain becomes aligned perpendicularly to the external magnetic field.

When unpolarized light from the YSO passes through the dust cloud (containing the aligned grains) the light is absorbed more along the long axis of the grains than along the shorter. This causes the light to become polarized at an angle perpendicular to the long axis of the grain, and thus parallel to the projection of the magnetic field as seen from the Earth. The degree of this polarization depends on both the relative number of aligned grains in the cloud and on the geometry of the aligned grains. A greater number of aligned grains will result in greater polarization, and ellipsoidal (or cylindrical) grains will polarize light to a higher degree than spherical grains.

In addition, the extent to which the radiation is absorbed differs slightly between the long and short axes of the grains, which causes a shift in the peak polarization to longer wavelengths relative to the extinction maximum. This effect has been seen in other YSOs (see eg. Hough et al., 1996), and is considered strong evidence that polarization is indeed caused by aligned grains.

Many YSOs have a deep absorption feature at 3.1 mm attributed to ``astronomical ice.'' This feature has been well-studied in many objects using spectropolarimetric techniques, which have shown an excess in polarization above the continuum. This continuum can be described by the equation

also known as the Serkowski law (Serkowski, Mathewson, & Ford 1975; Whittet et al. 1992), or by a power law with an index of 2 (Hough et al. 1996). In the original Serkowski law K = 1.15 (Serkowski, Mathewson, & Ford 1975), but Whittet et al. (1992) revised this to K = 0.01 ± 0.05 + (1.66 ± 0.09) l_max.

2.2 Spectropolarimetry With UKIRT's IRPOL2 Module

The 3.8 m United Kingdom Infrared Telescope (UKIRT) is equipped with a cooled grating spectrometer CGS4, which is designed for spectroscopy in the 1-5 mm range of the electromagnetic spectrum. The University of Hertfordshire designed and built IRPOL, an infrared polarimetry module to be used for both CGS4 and IRCAM3, UKIRT's infrared camera. IRPOL was recently re-designed and upgraded to IRPOL2 in order to increase the sensitivity, polarization accuracy and reliability of near-infrared polarimetry at UKIRT.

Spectropolarimetry at UKIRT works as follows: the incoming beam passes through a rotatable waveplate located at the Cassegrain focus. This waveplate is set to one of four positions for polarimetry: 0^°, 45^°, 22.^°5 and 67.^°5². The beam then passes through a Wollaston prism made of magnesium fluoride, MgF₂, which splits the beam into two orthogonally oriented beams, the so-called extraordinary and ordinary beams, also known as the e and o beams, which diverge at an angle of 2.3 degrees. The beams are split into spectra in CGS4, and are then recorded by the CGS4 InSb 256 × 256 array. The beams are separated by roughly 15 pixels on the array, this distance dependant on the wavelength.

In a typical CGS4/IRPOL2 observing sequence, the object is first observed with the waveplate at 0^°. The waveplate is rotated to 45^°, and another observation is made. The telescope is then nodded so that the spectra fall on different rows, another observation made³, the waveplate rotated back to 0^°, and another observation made. Observations are then made at waveplate positions of 22.^°5 and 67.^°5, after which the telescope is nodded back to its original position, and observations at 67.^°5 and 22.^°5 are again made. This is an efficient observation sequence in which the waveplate is rotated five times, and the telescope nodded twice.

In the data reduction process, the sky observations are subtracted from the object observations at the corresponding waveplate position. This causes a first-order subtraction of the sky, and produces four spectra on the image: a positive and negative spectrum for each of the e and o spectra. This subtraction also helps to improve the signal-to-noise ratio of the final spectrum. The spectra are then extracted from this image, and e and o spectra are formed for each of the four waveplate positions.

From these spectra the Stokes parameters, Q and U, can then be calculated. These two parameters are used to describe the state of polarization for an electromagnetic wave. In the following equations, e₀ refers to the e spectrum at the 0^° waveplate position (and similarly, e₄₅ for the e spectrum at 45^°, etc.), and I refers to the total intensity of the spectrum (found by adding the e and o spectra at a single waveplate position). For relatively strong signals, the ratio method is used:

For faint or noisy sources, the difference method is used:

Similar equations are used to calculate the u Stokes parameter, substituting the 22.^°5 and 67.^°5 positions for the 0^° and 45^°, respectively.

Once q and u have been calculated, the degree of polarization, p, and position angle, q, can be calculated using the following equations:

2.3 About W33A

W33A (R.A. 18 14 39.8, Decl. -17 51 59, 2000) is thought to be a protostar embedded in a dense molecular cloud (Capps, Gillet, & Knacke 1978). At infrared wavelengths it appears point-like, but may be extended at 2 mm. Its infrared spectrum from 1 to 10 mm shows two deep absorption features, one at 3.1 mm attributed to H₂O ice, and the other at 9.6 mm caused by silicates. Willner et al. (1982) give a value for the optical depth of the silicate band of 7.8; the H₂O band has not been fully resolved, but Willner et al. give t_3.1 > 5.4, and Joyce & Simon (1982) estimate t_3.1 ~ 5. Between 2.5 and 4 mm W33A shows a number of absorption features also seen in other YSOs. The deep absorption feature at 3.1 mm has a broad wing at wavelengths greater than 3.3 mm; this wing can be explained with various compounds. Léger et al. (1983) proposed that this long-wavelength wing is caused by large H₂O ice-coated grains. A mixture of NH₃ and H₂O ice has also been suggested (Merrill, Russell, and Soifer, 1976). C-H vibrations in hydrocarbons also produce absorptions in the 3.3 to 3.5 mm range of the long-wavelength wing. Features at 3.54, 3.85, and 3.94 mm have been attributed to methanol found in a H₂O:CH₃OH:CO:NH₃ = 100:50:1:1 mixture of ``astronomical ice'' (Allamandola et al. 1992). Another feature at 3.47 mm is tentatively attributed to tertiary C-H stretching in carbonaceous materials in a diamond-like structure.

Previous spectroscopic and spectropolarimetric studies of W33A have not been able to obtain data in the 3.1 mm ice feature, and thus no excess in polarization over the continuum has been recorded. Hough et al. (1989) found that the polarization in the long-wavelength (3.4 to 4 mm) wing shows no significant increase with decreasing wavelength, as the Serkowski formula (equation (1)) predicts, and which has been seen in other protostellar objects (see eg. Chrysostomou et al. 1996a). Two explanations for this were given: technology at the time would not allow for accurate measurements near the deep ice feature, or the presence of a bluer source 3'' south of the main IR source could be diluting the measured polarized flux at lower wavelengths. Little change in position angle was also detected, remaining relatively constant at 72^°.

W33A also has features in the 4.5 to 4.8 mm wavelength range that are not studied in this paper. Chrysostomou et al. (1996b) detected a polarization excess across absorption features due to XCN and CO. They also showed that the peak in polarization in both features were shifted to longer wavelengths relative to the corresponding peaks in optical depth. This is expected if aligned grains are the cause of the polarization (Kobayashi et al. 1980). They regarded this as definitive proof that XCN and CO mantled grains are aligned along the line of sight to W33A. No such observations have been made with features near the 3.1 mm ice feature.

3. Observations

Observations were made on the night of 1 June 1996 with the cooled grating spectrometer CGS4 on the 3.8 United Kingdom Infrared Telescope on Mauna Kea, Hawaii. The short focal length (150 mm) camera and 150 lines mm^-1 grating were used, giving a spatial resolution of 1.23'' pixel^-1 and spectral resolution (l/ Dl) of ~ 2500. The UKIRT infrared polarimeter module IRPOL2 was placed upstream of CGS4. Observations of W33A were made at 6 grating positions to fully cover the 3.1 mm ice feature. See Table for complete details of the observations.

Observations were taken in the sequence described in Section 2.2, above. In addition, flat-field frames were taken at each grating position, which were used to divide out pixel-to-pixel variations for each observation. Wavelength calibration was done by observing emission lines from internal argon and xenon lamps.

After the e and o spectra were extracted for each waveplate position, they were added to obtain the total intensity spectrum. This spectrum was flux calibrated by dividing through by the spectrum from a standard star at corresponding wavelengths, then multiplying the result by a blackbody spectrum with the same temperature as the standard star. This resulted in a spectrum with flux units of Janskys, which were then converted to units of W m^-2 mm^-1.

To determine the state of polarization, both the difference and ratio methods were used to obtain the q and u Stokes parameters. For the observations at 2.155, 2.485, 2.95, and 3.25 mm the difference method was used, as these observations were made in faint and noisy regions of the spectrum. For the observations at 3.55 and 3.85 mm the ratio method was used for these stronger signals. Both methods were used at 3.55 mm, and the resulting polarization spectra were identical.

Observations at 3.55 and 3.85 mm showed a periodic ripple, probably caused by a slight misalignment in the internal optics in IRPOL2. This ripple has been seen in observations of other objects, and is wavelength dependant. It was removed by identifying the period of the ripple in the q and u spectra by means of a Fourier analysis. These periods were removed from the Fourier transforms, and the spectra were then reconstituted. The resulting spectra had the ripple removed entirely, leaving the real spectra behind.

After the q and u spectra were calculated, some of the spectra were binned in an attempt to clean up noisy sections, details of which can be found in Table . The spectra are normally 256 pixels across, so the two wavelengths that have 256 bins were not binned; the states of polarization were calculated directly from the original data.

After removing the periodic ripple and binning the spectra, the state of polarization was calculated using Equations 6 and 7, above. The resulting spectra were merged together to produce the full spectrum from 2 to 4 mm. The spectrum at 3.55 mm was used as a reference, and all other spectra were scaled to match with this reference. Differences in spectra were on the order of 5%, and were most likely the result of small centering and tracking errors.

The efficiency of the Wollaston prism is wavelength dependant. Thus, the degree of polarization was corrected for this by dividing the calculated polarization by a theoretical efficiency correction:

where l_° is equal to the central wavelength of the prism, or 3.52 mm. This correction factor slightly raises the polarization at wavelengths on either side of 3.52 mm.

4. Results and Discussion

The results of the spectropolarimetry are shown in Figures and . Included in the degree of polarization plot are values from Hough et al. (1989).

The extreme depth of the 3.1 mm ice feature is clearly seen in Figure 1, as it spans three orders of magnitudes, in comparison to another YSO, the Becklin-Neugebauer object in OMC-1, which spans only one order of magnitude (Hough et al. 1996). The dual nature of the feature is also evident, with a pronounced flattening out of the feature at wavelengths longer than 3.3 mm. The absorption feature attributed to carbonaceous material in diamond-like structure is visible at 3.47 mm, as are methanol features at 3.54 and 3.94 mm.

The dashed curve in the flux plot in Figure 1 is a blackbody curve with T_eff(K) = 623 ±4. This value is similar to those used for other YSOs, ranging from 835 to 360 K (Smith, Sellegren, & Tokunaga 1989). This blackbody curve was fit to points in the regions 2.33 to 2.46 mm and 3.8 to 3.9 mm, which were assumed to be the continuum.

The degree of polarization shows some excess across the feature. Attempts to fit both the Serkowski law (Equation (1)) and a power law with index 2 failed. However, fitting with a power law with index 1 was able to fit to the polarization continuum, which was taken to be the regions 2.2 to 2.5 mm and 3.7 to 4 mm. This power law is shown as the dashed line in Figure 2. It is currently unknown why the continuum cannot be fit with either of the two equations that have been used for other YSOs.

The position angle of polarization shows almost no change across the 3.1 mm feature. There may be some evidence of an increase across the feature, but the data are too noisy to make any conclusive statements. The slight downturn at 3.5 mm may be real, but it should be noted that two spectra are joined near this wavelength, so a slight mismatch may cause this apparent structure.

Using the fitted blackbody flux I_BB in the flux plot to calculate the optical depth t of the feature with the equation

gives the optical depth spectrum shown in Figure . Also plotted in this figure is the polarization excess, Dp(l), which is found by subtracting the continuum polarization shown in Figure 2 from the observed polarization.

From Figure 3 the optical depth of the 3.1 mm ice feature is found to be t_3.1 = 6.2 ±0.6. This value is consistent with previous estimations that give t_3.1 > 5.4 (Willner et al. 1982). The uncertainty in this value is due to the low signal-to-noise ratio at the bottom of the feature. The long-wavelength wing is also seen as a flattening out of the optical depth at wavelengths longer than 3.3 mm. Slight peaks at 3.47 and 3.54 mm are also evidence of diamond-like material and methanol, respectively.

Figure 3 also shows an increase in polarization across the feature. As the spectra used to calculate the degree of polarization were very noisy, much of the data in the feature was masked. No peak is seen, so a comparison between the peak optical depth and peak polarization cannot be made. Gaussian curves were fit to the to the optical depth and polarization excess was made, but the results were inconclusive.

Figure shows the polarization excess and optical depth across the 3.47 and 3.54 mm features. The polarization excess was determined by fitting a second-order polynomial to points in the regions from 3.4 to 3.45 mm and 3.6 to 3.7 mm. The optical depth was determined by fitting an exponential curve to points in the regions from 3.3 to 3.4 mm and 3.6 to 3.7 mm, then using Equation 9 to calculate t. Polarization excess data have been binned into 5-pixel elements.

The peaks at 3.47 and 3.54 mm are easily visible in Figure 4, reproducing the results from Allamandola et al. (1992). The optical depths of these two features are 0.35 and 0.42, respectively, compared to values of 0.3 and 0.39 from Allamandola et al. Differences in these values are due mostly to differing baselines. Because the spectrum of W33A becomes noisier at wavelengths shorter than 3.4 mm, a baseline is difficult to reproduce from one data set to another.

There is also a possible polarization excess in this portion of the spectrum. An excess can be seen extending from 3.5 to 3.6 mm. This excess peaks at 3.55 mm, approximately 0.01 mm higher than the 3.54 mm feature attributed to methanol. According to Kobayashi et al. (1980) the wavelength at which peak polarization occurs will be at a longer wavelength than that at which the peak optical depth occurs. Should this polarization excess in W33A be real, it is strong evidence that methanol mantled grains are aligned along the line of sight to W33A. Another peak may also be seen at 3.49 mm, 0.02 mm longer than the 3.47 mm diamond feature. This second peak appears close to a noisy section of the spectrum, so its identification with the 3.47 mm feature is very tentative at best.

Figure 5 shows the polarization excess and optical depth across the 3.97 mm feature. The polarization excess was determined by fitting a straight line to points in the regions 3.8 to 3.9 mm and 4 to 4.03 mm. The optical depth was determined by fitting a blackbody curve with T_eff(K) = 239 to the same regions as for the polarization excess, then using Equation 9 to calculate t.

The 3.94 mm feature is easily seen, with an optical depth of approximately 0.15. There is, however, no identification of a polarization excess near this feature. This is in apparent contradiction to the tentative identification of an excess across the 3.54 mm feature. If methanol mantled grains are aligned in W33A, there should be polarization excesses at both 3.54 and 3.94 mm. This discrepancy is as yet unexplained.

As previous observations of W33A have shown that CO and XCN features show a shift in peak polarization, implying that CO and XCN mantled grains become aligned, similar results should be seen for the CH₃OH and ``diamond'' features. The results presented in this paper show some polarization excess across the 3.54 mm CH<sub>3</sub>OH feature, and a possible excess across the 3.47 mm ``diamond'' feature, but no excess is seen across the 3.94 mm CH₃OH feature. It may be the case that the 3.54 mm polarization excess is a false identification, and CH₃OH mantled grains are not being aligned with the magnetic field. This hypothesis is puzzling, as laboratory studies have shown that a mixture of H₂O and CH₃OH can best explain the methanol features (Allamandola et al. 1992). This paper shows a polarization excess across the H₂O feature, and if the H₂O and CH₃OH are mixed, then a corresponding polarization excess across the methanol features at 3.54 and 3.94 mm should be seen. It is more likely that the non-detection of a polarization excess across the 3.94 mm feature is incorrect, and higher signal-to-noise observations could possibly reveal such an excess.

5. Conclusions

Spectropolarimetric observations between 2.0 and 4.1 mm of the young stellar object W33A have been presented. The deep ice absorption feature at 3.1 mm has been resolved for the first time, giving an optical depth of 6.2 ± 0.6, consistent with previous estimations. Absorption features attributed to methanol (at 3.54 and 3.94 mm) and diamond-like carbonaceous material (at 3.47 mm) are also confirmed. A polarization excess is seen across the 3.1 mm feature, but due to the extreme depth of this feature no peak in the polarization was found, and thus no confirmation of the dicroic nature of the polarization can be made. Polarization structure is seen in the long-wavelength wing of the ice feature, and is tentatively attributed to methanol. This polarization does show a peak which occurs at longer wavelengths than the peak optical depth, which is predicted by theory, and is considered strong evidence that the polarization is caused by aligned grains. However, a polarization excess is not seen across the 3.94 mm methanol feature, in seeming contradiction to these claims. In addition, a very tentative identification of polarization structure at 3.49 mm is associated with diamond-like material.

5.1 Recommendations

Because of the extreme depth of the 3.1 mm ice feature in W33A, spectropolarimetric observations near this wavelength are difficult to obtain. However, the recently upgraded CGS4 on UKIRT should be able to make better observations of features in the long-wavelength wing of the feature. Higher signal-to-noise observations should be made of this section of the spectrum in order to confirm the alignment of grains in W33A. Also, it is puzzling why no polarization excess across the 3.97 mm feature is seen; these observations could be repeated to decipher the apparent contradiction.

6. Acknowledgements

I would like to thank Antonio Chrysostomou for giving me the opportunity to work with him on this project. Acknowledgements also go to Stuart Ryder for allowing this project to proceed past the original two month deadline, and to the staff of the JAC for providing a welcome environment in which to work.

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Footnotes:

¹ Numerous theories have been proposed to explain how the grains become spun up, but they all have various flaws. Polarization observations show that the grains do become aligned with magnetic fields, and thus are somehow spun up, but a suitable theoretical explanation for this spinning-up process is currently lacking

² Theoretically only two waveplate positions should be needed, 0^° and 45^°. However, the Wollaston prism attenuates the beam such that the optical path that each beam takes through the prism is not identical. For example, for an unpolarized source the e and o beams would be equal, but after passing through the prism they are not. Observations at four positions are needed to compensate for this attenuation.

³ This observation is known as a sky observation.